It is a Sig 522 Pistol, with an SBR stamp (in order to have a butt-stock on that shorter barreled firearm), and a folding stock added.
If you don't want to click the link, or if you need help understanding what you're seeing, then here is a Cliff's Notes verion. You can see some pictures of this set-up here. Unfortunately, this same rifle might have to pull double-duty as a light-power fighter. I'd also like some accuracy, with the assumption that I must be able to hit a tree-rat for food. This makes me sad because reliabilty would theoretically go to a bolt-action, which is mostly the opposite of compact. Top priorities go to reliability, then compactness. For a SHTF survival rifle, I'd look at a few characteristics.
